Principal band gaps and bond lengths of the alloy (Al xGa 1− x) 1− zIn zP yAs 1− y lattice matched to GaAs

Abstract

The principal band gaps ( E( Γ) ,E( L), and E( X)) and bond lengths ( d( x, y, z))of the alloy (Al x Ga 1− x ) 1− z In z P y As 1− y (where, 0 < x + z < 1, and 0 < y < 1) are calculated over the entire composition range based on the first order correlated function expansion (CFE) scheme. Defining the lattice strain parameter as ϵ = | d ⁡ ( x , y , z ) − d ⁡ ( 0 , 0 , 0 ) | d ⁡ ( 0 , 0 , 0 ) × 100 % , it is found that a good quality of alloy (defining ϵ < ∼ 0.5%) can be obtained in the composition region : 0 < x < ∼ 0.3, 0 < y < ∼ 0.2 and 0 < z < ∼ 0.1. The first order CFE lattice matching relations and corresponding band gaps for the alloy on the GaAs substrate are also determined. It is found that the principal band gaps of the alloy (Al x Ga 1− x ) 1− z In z P y As 1− y lattice matched to GaAs covers band gap ranges: 1.45 eV E < ( Γ) 2.69 eV, 1.80 eV < E( L) < 2.38 eV, and 1.97 eV < E( X) < 2.20 eV, while the direct band gap covers from 1.45 eV to 2.05 eV. Our theoretical prediction was compared with the existing experimental data.